In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves...

function theorem. The number B is called the Bloch's constant. The lower bound 1/72 in Bloch's theorem is not the best possible. Bloch's theorem tells us...

periodic function, with the same periodicity as the crystal lattice. Bloch's theorem proves that the solutions to this differential equation can be written...

a simple kinetic-plus-potential form.: 134  These conditions imply Bloch's theorem, which states ψ n ( x ) = e i k ⋅ x u n k ( x ) , u n k ( x + a ) =...

is useful to make the Fourier series of the potential when applying Bloch's theorem. First, we may write any arbitrary position vector r {\displaystyle...

such as crystals in condensed matter physics, the result is known as Bloch's theorem. Note that the solutions of the linear differential equation form a...

Picard's theorem.) His proof of this theorem contained gaps (which he recognized), and later the theorem was known as "Bloch's conjecture". Bloch's conjecture...

{k} \cdot \mathbf {R} }\psi (\mathbf {r} )} This result is known as Bloch's Theorem. In the passive transformation picture, translational invariance requires...

stems from the description of waves in a periodic medium given by Bloch's theorem, in which it is found that the solutions can be completely characterized...

special case of electron waves in a periodic crystal lattice using Bloch's theorem as treated generally in the dynamical theory of diffraction. Every...

periodic potential. The solutions in this case are known as Bloch states. Since Bloch's theorem applies only to periodic potentials, and since unceasing...

principle, Picard's theorem corresponds to Schottky's theorem, and Valiron's theorem corresponds to Bloch's theorem. Based on his Principle, Bloch was able to...

the potential is a periodic function with a period a. According to Bloch's theorem, the wavefunction solution of the Schrödinger equation when the potential...

Felix Bloch (/blɒk/; German: [blɔx]; 23 October 1905 – 10 September 1983) was a Swiss-American physicist and Nobel physics laureate who worked mainly...

quantum-mechanical justification was given a year later (1928) by Bloch's theorem: an unbound electron moves in a periodic potential as a free electron...

condition and plugging in Schrödinger's equation results in a proof of Bloch's theorem, which is particularly important in understanding the band structure...

In mathematics, the norm residue isomorphism theorem is a long-sought result relating Milnor K-theory and Galois cohomology. The result has a relatively...

Bishop–Cannings theorem (economics) Blakers–Massey theorem (homotopy theory) Blaschke selection theorem (geometric topology) Bloch's theorem (complex analysis)...

physics, Nanoscale and mesoscopic physics, Polymer physics BCS theory, Bloch's theorem, Density functional theory, Fermi gas, Fermi liquid theory, Many-body...

independent electron approximation is still in effect. As shown by Bloch's theorem, introducing a periodic potential into the Schrödinger equation results...

coordinates (the Born–Oppenheimer approximation). The code also makes use of Bloch's Theorem which means a wavefunction of a periodic system has a cell-periodic...

crystal Seismic metamaterials Split-ring resonator Tunable metamaterials Bloch's theorem Casimir effect Dielectric Electromagnetism EM radiation Electron mobility...

model and the nearly-free electron model, where it is used alongside Bloch's theorem. In quantum mechanics, this approximation is often used to simplify...

a solid need not be carried out with full rigor as in the original Bloch's theorem but, rather, first-principles calculations are carried out only at...

pioneered in 1929 by Rudolf Peierls, who analyzed the Hall effect using Bloch's theorem, and demonstrated that a nearly full and a nearly empty Brillouin zones...

which the effect had first been observed. Anderson impurity model Bloch's theorem Electronic band structure Solid-state physics Bose–Hubbard model t-J...

via that envelope wave, usually using the "physics definition". See Bloch's theorem for further details. A moving wave surface in special relativity may...

potential; see Bloch's theorem. Named after French mathematician André Bloch an analytic function in the unit disc which is an element of the Bloch space. This...

physics, Nanoscale and mesoscopic physics, Polymer physics BCS theory, Bloch's theorem, Density functional theory, Fermi gas, Fermi liquid theory, Many-body...

Schrödinger equation is often written for functions of momentum, as Bloch's theorem ensures the periodic crystal lattice potential couples Ψ ~ ( p ) {\displaystyle...